A simple model of the reflection effect for the interacting binaries and extrasolar planets

TL;DR

This paper introduces a simple, comprehensive model for the reflection effect in irradiated objects like exoplanets, accounting for shape, heat redistribution, and observational effects, and applies it to known transiting exoplanets.

Contribution

It develops a new model for the reflection effect that includes shape, heat redistribution, and Doppler shifts, improving analysis of exoplanet light curves and spectra.

Findings

Model reproduces observations of HD189733b, WASP12b, and Wasp-19b.

WASP-12b and Wasp-19b have low Bond albedo and low heat redistribution.

Departures from spherical shape can reach up to 14%. in some exoplanets.

Abstract

Extrasolar planets are a natural extension of the interacting binaries towards the companions with very small masses and similar tools might be used to study them. Unfortunately, the generally accepted treatment of the reflection effect in interacting binaries is not very suitable to study cold objects irradiated by hot objects or extrasolar planets. Our simple model of the reflection effect takes into account the reflection (scattering), heating and heat redistribution over the surface of the irradiated object. The shape of the objects is described by the Roche potential and limb and gravity darkening can be taken into account. The orbital revolution and rotation of the planet with proper Doppler shifts for the scattered and thermal radiation are also accounted for. Subsequently, light-curves and/or spectra of exoplanets were modeled and the effects of the heat redistribution, limb darkening/brightening, (non-)grey albedo, and non-spherical shape were studied. Recent observations of HD189733b, WASP12b, and Wasp-19b were reproduced reasonably well. HD189733b has low Bond albedo and intense heat redistribution. Wasp-19b has low Bond albedo and low heat redistribution. We also calculate the exact Roche shapes and temperature distribution over the surface of all 78 transiting extrasolar planets known so far. It is found that the departures from the sphere vary considerably within the sample. Departures of about 1% are common. In some cases: WASP-12b, WASP-19b, WASP-33b departures can reach about 14, 12, and 8%, respectively. The mean temperatures of these planets also vary considerably from 300 K to 2600 K. The extreme cases are WASP-33b, WASP-12b, and WASP-18b with mean temperatures of about 2600, 2430, and 2330 K, respectively.